Last night my bathroom basin/sink leaked by where the drain pipe joins the bottom of the sink - when I examined the flange at the drain hole - it had corroded at the threads/joint and basically broken off -

I may be using the wrong terminology -
so here are some pics -

There is obviously a gap now at the joint -

Close up -

I thought it might be simple to repair - just take the flange to a Home Depot/Lowes and ask what I need to repair this ......

But I thought I'd ask here first
- what parts should I be getting, please?
and any hints/advice in making this repair.

Also the pop-up plug is now broken at the point where the horizontal pivot rod/actuator connects
- what do I do to ensure that is adjusted correctly for the new replacement - so I don't break the new one too, and the plug seals well enough so it does not leak?

As long as there is no damage to the sink itself, you probably only need to replace the pop up drain assembly. This is only an example. You can get them in most finishes, and probably cheaper than this one from HD...click this link and it will show it to you...

A handy tip... Get a small tube of plumber grease while you're at it, and grease the threads before installing it. It only costs about $3 and will really help the rubber seal slide up against the sink and will help when tightening the nut. Also, some grease around the ball of the pop-up lever will help it operate smoothly.

And don't forget to use plumbers putty on the new drain. Just roll it in your hands to make a 1/2" to 3/4" thick snake and place it around the drain where it will meet the top of the sink. Unless you sink is cast it is probably fine. if there is damage to the sink you will 1 replace it or 2 need to rebuild the damage with epoxy. Not an easy task if your not experienced.

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I took just the top flange to a Lowes - and they don't sell just the flange - they had the entire kit - like Hack showed above - these were in the $11-$25 price range in the stores I looked in - they're 1-1/4" pop-up drain assemblies.

So far, I can't see much, if any, real difference between them (but I will use travelover's magnet tip) - I will probably just buy an entire assembly.

Fitting does seem commonsense - and I already have some plumbers' putty and teflon tape for the job.

Better quality have brass or stainless rods for the pop-up. Other differences are the tail piece that connects to the drain is plastic (the threads strip easily) or thinner metal (corrodes quicker), the seal around the stopper sometimes leaks (hear a trickle when the sink is full), and I could probably think of more. You get what you pay for.

If you hold the two of them, one in each hand, the more expensive one will weigh more. That's because they put more brass/stainless into it.